Allometry Results

Data

Presented are two blocks of allometry data from my orchard scaling project (2012-2013) conducted at Kaysville Research Farm, USU. I sampled five 24 year old tart cherry (Prunus cerasus Montmorency, P. mahaleb) from one block and 19 8 year-old apples (Malus domestica “Golden Delicious”) from one block with various rootstocks. BranchSegments.csv (branch_size) contains the size and orientation data for all trees sampled at a branch-level. TreeSummary.csv (tree_sum) contains the size and orientation data for all trees sampled at a tree-level. Listing of fields represented in the data are located at the end of this dococument for both data files. Data is analysed using Standardized Major Axis (SMA; aka reduced major axis) with R-package ‘smatr’.

Frequency Distributions

Length Histograms

Histograms for segment length [cm], path length, and subtree length levels. Sample size is listed next to title. There are 5 cherry and 19 apple individuals represented. The Biggest Apple is the largest rootstock (‘PiAu’) with 3 individuals represented. The Smallest Apple is the smallest rootstock (‘B9’) with 4 individuals represented.

I’d like to use this data to determine if the tree is fractal (Log-Log or Log-Linear), but my notes are unclear how exactly to do that. Please, help. *

Segment Length

Segment length is the distance of a branch unit bounded by two major branching events. plot of chunk length_hist

Path Length

Path length is the total length of a target branch and the longest continuous length of succeding branches. The calculation includes terminal twigs when the data is available. plot of chunk pathlength_hist

Subtree Length (includes terminal twigs when possible)

Subtree is the diameter of a given branch segment, and the total length, total surface area, and total volume of all branch segments distal to that branch segment.

plot of chunk subtreelength_hist

Diameter Histograms

Histograms for diameter [mm] at an individual level. Sample size is listed next to title. There are 5 cherry and 19 apple individuals represented. The Biggest Apple is the largest rootstock (‘PiAu’) with 3 individuals represented. The Smallest Apple is the smallest rootstock (‘B9’) with 4 individuals represented.
plot of chunk diameter_hist

Mass Histograms

Histograms for segment mass, total segment mass, and total subtree mass. Sample size is listed next to title. There are 5 cherry and 19 apple individuals represented. The Biggest Apple is the largest rootstock (‘PiAu’) with 3 individuals represented. The Smallest Apple is the smallest rootstock (‘B9’) with 4 individuals represented.

Segment Mass

plot of chunk mass_hist

Total Segment Mass

Total Segment Mass is the the sum of all major branch segments. Terminal twigs are not included. plot of chunk totmass_hist

Subtree Mass

Subtree mass is the total sum of all major branch and twig segments. Twig mass is added to Total Segment Mass. plot of chunk subtreemass_hist

Daughter/Parent Branch Area Ratio Histograms

The Branch Area Ratio is sum of daughter branch surface areas divided by the surface area of their parent branch. plot of chunk arearatio_hist

Scaling Relationships

Length ~ Diameter

Expected Exponent: Flow Similarity = 2 (peripheral / fruiting branches); Biomechanical = 2/3 (basal / scaffold branches)

Tree Height [Estimated: 0.74 +/- 0.12, R2 = 0.849]

plot of chunk Diameter_Height_output

Segment Length [Estimated: 0.90 +/- 0.06, R2 = 0.005]

plot of chunk diameter_length_output

Path Length [Estimated: 0.86 +/- 0.04, R2 = 0.448]

plot of chunk diameter_path_output

Total Subtree Length [Estimated: 1.72 +/- 0.10, R2 = 0.230]

plot of chunk diameter_totlength_output

Surface Area ~ Volume

Expected Exponent: Flow Similarity = 3/4 ; Biomechanical = 5/8

Segment Level [Estimated: 0.62 +/- 0.01, R2 = 0.918]

plot of chunk area_volume_output

Subtree Level [Estimated: 0.72 +/- 0.01, R2 = 0.969]

plot of chunk totarea_totvolume_output

Diameter ~ Volume

Expected Exponent: Flow Similarity = 1/4 ; Biomechanical = 3/8

Segment Level [Estimated: 0.44 +/- 0.01, R2 = 0.841]

plot of chunk diameter_volume_output

Subtree Level [Estimated: 0.38 +/- 0.01, R2 = 0.938]

plot of chunk diameter_totvolume_output

Length ~ Volume

Expected Exponent: Flow Similarity = 1/2 ; Biomechanical = 1/4

Segment Level [Estimated: 0.39 +/- 0.03, R2 = 0.219]

Subtree Level [Estimated: 0.67 +/- 0.04, R2 = 0.294]

plot of chunk totvolume_totlength_output

Diameter ~ Surface Area

Expected Exponent: Flow Similarity = 1/3 ; Biomechanical = 3/5

Segment Level [Estimated: 0.71 +/- 0.03, R2 = 0.586]

plot of chunk diameter_area_output

Subtree Level [Estimated: 0.53 +/- 0.01, R2 = 0.859]

plot of chunk diameter_totarea_output

Length ~ Surface Area

Expected Exponent: Flow Similarity = 2/3 ; Biomechanical = 2/5

Segment Level [Estimated: 0.64 +/- 0.03, R2 = 0.491]

plot of chunk area_length_output

Subtree Level [Estimated: 0.93 +/- 0.05, R2 = 0.391]

plot of chunk totarea_totlength_output

Length ~ Mass

Tree Level [Estimated: 0.30 +/- 0.05, R2 = 0.849]

plot of chunk Height_Mass_output

Branch Level [Estimated: 0.35 +/- 0.1, R2 = 0.632]

plot of chunk length_mass_output

Mass ~ Diameter

Tree Level [Estimated: 2.49 +/- 0.18, R2 = 0.974]

plot of chunk Diameter_Mass_output

Branch Level [Estimated 2.48 +/- 0.05, R2 = 0.905]

plot of chunk diameter_mass_output

Mass ~ Volume (Wood Density)

Segment Level [Estimated: 0.95 +/- 0.01, R2 = 0.962]

plot of chunk mass_volume_output

Subtree Level [Estimated: 0.95 +/- 0.01, R2 = 0.977]

plot of chunk totmass_totvolume_output

Diameter ~ No of terminal branches

[Estimated: 0.69 +/- 0.03, R2 = 0.429

plot of chunk diameter_tottwigs_output

Surface Area ~ No of terminal branches

[Estimated: 1.29 +/- 0.05, R2 = 0.669]

plot of chunk totarea_tottwigs_output

Diameter Ratio

The Diameter Ratio is a pairwise relationship of a daughter segment to its parent.

[Estimate: 0.68 +/- 0.03, R2 = 0.569]

plot of chunk diameterratio_output